Why do cosec, sec & cot exist? eventhough the main role is played by sin,cos & tan, then what is the purpose of cosec, sec & cot?
Answers
Answer:
Naming Ratios
For 3 numbers there are 6 ratios that can be made. Sine, Cosine and Tangent name 3 of the ratios, and the three you mentioned allow us to name all 6 ratios.
Avoiding division.
Example:
If we know that the angle of elevation to the top of a 12 meter tall building is
40
∘
and we want to find the distance to the building, call it
x
we could use
12
x
=
tan
40
∘
so
x
=
12
tan
40
∘
Now we get a decimal approximation for
tan
40
∘
≈
0.8391
and do the division.
OR use
x
12
=
cot
40
∘
so
x
=
12
cot
40
∘
=
We get
cot
40
∘
≈
1.1918
and multiply.
Also, in calculus many of us prefer to work with multiplication of functions rather than division and prefer, for example,
y
=
x
3
cot
x
rather than
y
=
x
3
tan
x
Answer:
Cosec sec and cot are sub T ratio on main T ratio for calculations to be the perfect